I’m wondering what happens if I graciously skip the background check in the interest of diversity, and one of my new hires commits the same crime he committed before on a customer or another employee.
The victim then sues me because if I had done a simple background check, I would have seen the person’s prior arrest record.
Damned if you do, damned if you don’t.
That's not the way I read it. I see nothing to prevent you from making a background criminal check. Just that you may not refuse to hire on the results of that check. But...
You can then cover yourself by writing the EEOC informing them that you have a potential serious criminal, but you are not refusing to hire him/her/it only because the EEOC forbids you to do so.
Then, when you get sued...